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Pierce J.F. — Singularity Theory, Rod Theory, And Symmetry Breaking Loads
Pierce J.F. — Singularity Theory, Rod Theory, And Symmetry Breaking Loads



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Название: Singularity Theory, Rod Theory, And Symmetry Breaking Loads

Автор: Pierce J.F.

Язык: en

Рубрика: Математика/

Серия: Lecture Notes in Mathematics

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Издание: 1st edition

Год издания: 1989

Количество страниц: 184

Добавлена в каталог: 12.09.2008

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
Action, group      12
Action, group on $W^{r, 2}$ spaces      65
Action, group on internal energy function      68
Action, group on load spaces      58 60 62
Action, group, coadjoint      58
Action, group, convective representation      22
Angles (Euler)      11
Antman, S.      2 4 6 68
Betti form      78
Bifurcation problem      85
Bifurcation problem, finite-dimensional      111 115
Bifurcation problem, symmetric      2 116
Bilinear form      45 55 64
Body, constrained      7
Body, material      7
Body, three-dimensional      35
Buzano, E.      2 164
Centerline      7
Centroids      7
Chillingworth, D.      2
Classification Theorem      134
Configuration(s), constrained      28
Configuration(s), constrained, group actions on      30
Configuration(s), constrained, manifold of      28
Configuration(s), equilibrating      84
Configuration(s), equilibrating, orbit of      85
Configuration(s), equilibrating, orbit of, neighborhood of      103
Configuration(s), Kirchhoff theory      9 24
Configuration(s), reference      35
Configuration(s), space of, Kirchhoff theory      9 24
Configuration(s), space of, special Cosserat theory      9 24
Configuration(s), special Cosserat theory      9 24
Configuration(s), straight      3
Configuration(s), three-dimensional      36
Configuration(s), trivial      5 84
Convective (representation), infinitesimal displacements      19 27
Cosserat theory, special, configurations      9 24
Cosserat theory, special, configurations, space of      9 24
Cosserat theory, special, infinitesimal displacements      13 25
Cosserat theory, special, infinitesimal displacements, space of      13 25
Cosserat theory, special, loads      40 63
Cosserat theory, special, loads, representation space      44 63
Crandall, M.      2
Critical point      76
Critical point, constrained      77
Cross section      7
Damon, J.      165
Decomposition theorem      99 100
Decomposition, representation spaces, infinitesimal displacement      78 91
Decomposition, representation spaces, load      80 92
Director (vectors)      7 44
Director (vectors), forces and moments, components of      43
Discriminant      150
Elastica      2
Elastostatic operator, convective representation      75
Elastostatic operator, symmetries      75
Euler angles      11
Euler field (operator)      73
Euler field (operator), convective representation      75
Euler field (operator), linearization      93
Euler field (operator), symmetries      75
Field, Euler      73
Force, three-dimensional, body      36
Force, three-dimensional, constraint      82
Force, three-dimensional, surface      36
Form, Betti      78
Form, bilinear      45 55 62
Form, canonical      132
Form, canonical, classification      13
Form, canonical, oriented      132
Form, canonical, unoriented      132
Function, internal energy      67
Function, internal energy, (in) Kirchhoff theory      68
Function, internal energy, (in) special Cosserat theory      68
Function, internal energy, group action on      68
Function, internal energy, representation      69
Function, potential      71
Function, potential, constrained      76
Function, potential, reduced      110 115
Function, potential, symmetries      72
Geymonat, G.      2
Golubitsky, M.      2 165
Group(s)      11
Group(s), (on) infinitesimal displacements      21
Group(s), (on) infinitesimal displacements, (on) constrained configurations      30
Group(s), (on) infinitesimal displacements, (on) internal energy      61
Group(s), (on) infinitesimal displacements, (on) loads      58
Group(s), action      see "Actions"
Group(s), action, (on) configurations      11
Group(s), isotropy      86
Group(s), isotropy, load      83
Group(s), material symmetry      69
Group(s), representations of, convective      22 58
Group(s), representations of, spatial      22 58
Hyperelastic (material)      68
Hypothesis, Kirchhoff      9
Hypothesis, material response      95
Infinitesimal displacements      13 25
Infinitesimal displacements, 3D      36
Infinitesimal displacements, constrained      29
Infinitesimal displacements, representation, convective      19 27
Infinitesimal displacements, representation, spatial      19
Infinitesimal displacements, space of      19 25
Invertibility condition      8
Isotropy, group, configuration      86
Isotropy, group, load      83
Isotropy, group, relations      87
Isotropy, transversal      69
Kirchhoff (theory)      3
Kirchhoff (theory), configuration      9 24
Kirchhoff (theory), configuration, constrained      28
Kirchhoff (theory), configuration, space of      9 24
Kirchhoff (theory), infinitesimal displacements, convective representation      27
Kirchhoff (theory), infinitesimal displacements, space of      19 25
Load(s), rod, a-priori      33
Load(s), rod, astatic      37
Load(s), rod, astatic, Kirchhoff theory      5
Load(s), rod, astatic, special Cosserat theory      38
Load(s), rod, dead      36 40
Load(s), rod, follower      165
Load(s), rod, live, 3D      59
Load(s), rod, perturbing, canonical form      13
Load(s), rod, perturbing, classification      13
Load(s), rod, perturbing, symmetric      117
Load(s), rod, perturbing, type (class)      134
Load(s), rod, representation space, Kirchhoff theory      54 63
Load(s), rod, representation space, Kirchhoff theory, decomposition of      93
Load(s), rod, representation space, special Cosserat theory      44 63
Load(s), rod, representations of, (as) forces and moments      43
Load(s), rod, representations of, convective      44
Load(s), rod, representations of, spatial      44
Load(s), rod, space of, Kirchhoff theory      54 63
Load(s), rod, space of, Kirchhoff theory, decomposition of      93
Load(s), rod, space of, special Cosserat theory      40 63
Load(s), rod, spaces of, Kirchhoff rod      54
Load(s), rod, spaces of, Kirchhoff rod, decomposition of      89
Load(s), rod, spaces of, special Cosserat theory      63
Load(s), rod, symmetric perturbing      117
Load(s), rod, symmetry-breaking      117
Load(s), rod, systems, dead      34
Load(s), rod, unperturbed      83
Load(s), rod, work done (Kirchhoff theory)      54
Load(s), rod, work done (Kirchhoff theory), convective representation      55
Load(s), rod, work done (Kirchhoff theory), spatial representation      55
Load(s), rod, work done by (special Cosserat theory)      40
Load(s), rod, work done by (special Cosserat theory), (as) forces and moments      42
Load(s), rod, work done by (special Cosserat theory), convective representation      45
Load(s), rod, work done by (special Cosserat theory), spatial representation      45
Load(s), three-dimensional      36
Load(s), three-dimensional, astatic      37
Load(s), three-dimensional, dead      36
Load(s), three-dimensional, work done by      37
Manifold(s), critical      123
Manifold(s), critical, classification of      134
Marsden, J.      2 46
Material body      7
Material cross section      7
Material point      7
Mechanics, symplectic      56
Moments, director components of      42
Morse function      140
Morse theory      140
Multiplication in $W^{r, 2}$      25
Multipliers, Lagrange      77 82
Operator, elastostatic      75
Operator, Euler      75
Operator, Euler, linearization      93
Orbit, (of) equilibrating configurations      85
Orbit, trivial      85
Perturbation(s), symmetric      117
Perturbation(s), symmetry-breaking      117
Perturbation(s), type (class)      134
Point, material      7
Poston, T.      2
Problem (rod)      85
Problem (rod), finite dimensional      111 115
Problem (rod), full      2 85 164
Problem (rod), orbit-breaking      1 112
Problem (rod), orbit-breaking, class $\alpha$      146
Problem (rod), orbit-breaking, class $\beta$      151
Problem (rod), orbit-breaking, class $\gamma$      152
Problem (rod), symmetric buckling      116
Problem (rod), symmetrically perturbed      116 118
Problem (rod), symmetry-breaking      117
Rabinowitz, P.      2
Representation, (of) rod loads, (as) forces and moments      43
Representation, (of) rod loads, convective      44 54
Representation, (of) rod loads, convective, decomposition of      80
Representation, (of) rod loads, spatial      44 54
Representation, infinitesimal displacements, convective      19 27
Representation, infinitesimal displacements, convective, decomposition of      78
Representation, infinitesimal displacements, spatial      19
Representation, space (for), (for) loads, $C^{k}$, Cosserat theory      40 63
Representation, space (for), (for) loads, $C^{k}$, decomposition of      80 92
Representation, space (for), (for) loads, $C^{k}$, Kirchhoff theory      54 63
Representation, space (for), infinitesimal displacements, Cosserat theory      19 27
Representation, space (for), infinitesimal displacements, decomposition of      78 91
Representation, space (for), infinitesimal displacements, Kirchhoff theory      19 27
Schaeffer, D.      2 165
Simo, J.      46
Space (of), dead loads      36
Space (of), infinitesimal displacements, Kirchhoff theory      19 27
Space (of), infinitesimal displacements, special Cosserat theory      19 27
Space (of), load representation, Kirchhoff theory      54 63
Space (of), load representation, special Cosserat theory      44 64
Space (of), rod loads, Kirchhoff theory      54 63
Space (of), rod loads, special Cosserat theory      40 63
Theorem, classification      134
Theorem, decomposition      99 100
Tubular neighborhood      103
Unfolding      3 120 165
Wan, Y.H.      2
Work, virtual, $W^{r, 2}$      64
Work, virtual, (done by) loads, dead, Kirchhoff theory      54 55
Work, virtual, (done by) loads, dead, special Cosserat theory      40 42 45
Work, virtual, three-dimensional      37
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